Locally repairable codes(LRCs) were proposed to reduce the repair degree in distributed storage systems. In particular, LRCs with availability are highly desirable for distributed storage systems, since this kind of codes provide the mechanism of local repair for code symbols and parallel reading of hot data.In this paper, we propose four types of(n, k, r, t)_q LRCs from combinatorial designs. We introduce several constructions of LRCs with strict availability and some constructions of...

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